Physics Exercises/Conservation of Linear Momentum

Exercises

Catapult recoil velocity

A motionless catapult was aimed horizontally and fired a 10.0 kg wood block due west at 50 m/s. If the catapult's mass was 250 kg, what is the recoil velocity of the catapult if friction is ignored?

Solutions

Catapult recoil velocity

Conservation of linear momentum is used to solve this problem. The sum of the momentum of the wood block plus the momentum of the catapult must equal the sum of their momentum before the object was fired, which is zero.

M = mass, V = velocity, c = catapult, w = wood block

$M_c{V}_c+M_w{V}_w=0$

$(250.kg)V_c+(10.0kg)(50.0m/s)=0$

$V_c=\frac{-(10.0kg)(50.0m/s)}{250.0kg}$

$V_c=-2.00m/s$

The negative sign indicates that the direction is opposite to the direction of motion of the wood block, which would be east.